The equation for the area of a square could be written: A=s^2 (4 points)

Question

1) Is this a linear or nonlinear function?

2) What are some of the values in the table where s is the side length and A is the area?

3) When you plot these points, is the graph increasing or decreasing?

4) What numbers would be included in the domain?

Answer 1

1. The equation \( A = s^2 \) is a nonlinear function. This is because the relationship between \( A \) and \( s \) involves squaring the variable \( s \), which means it does not form a straight line when graphed.

2. Here is a table of some values for \( s \) (side length) and corresponding \( A \) (area):

| \( s \) (side length) | \( A \) (area) | |--------------------|--------------| | 0 | 0 | | 1 | 1 | | 2 | 4 | | 3 | 9 | | 4 | 16 | | 5 | 25 |

3. When you plot these points, the graph is increasing. As \( s \) increases, \( A \) also increases, and because the function is quadratic, it will increase at an increasing rate.

4. The domain of the function \( A = s^2 \) is all non-negative real numbers, which can be expressed as \( [0, \infty) \). This is because the side length \( s \) cannot be negative (a square cannot have a negative length).